Optical design of a street lamp based on dual-module chip-on-board LED arrays Aiming Ge,1,* Jinlin Cai,1 Dehua Chen,2 Hongyun Shu,2 Peng Qiu,1 Junwei Wang,1 and Ling Zhu1 1
Department of Light Sources and Illuminating Engineering, School of Information Science and Engineering, Institute for Electric Light Sources, Fudan University, Shanghai 200433, China 2
Dongguan CLED Optoelectronic Technology Co., Ltd, Dongguan 523270, China *Corresponding author: [email protected] Received 2 June 2014; revised 27 July 2014; accepted 28 July 2014; posted 31 July 2014 (Doc. ID 213230); published 28 August 2014
We design and propose a compact street lamp based on dual-module chip-on-board LED. The street lamp is composed of six faceted reflectors. It can direct the luminous flux and form uniform illumination on the target area, and it effectively reduces power consumption. We have conducted both simulations and prototype measurements. The test results show good optical performance in that the uniformity of luminance reaches 0.58 for LED lamp zigzag arrangements and 0.60 for LED lamp double-side arrangements. The average luminance can fulfill the requirements in Chinese road lighting Standard CJJ45-2006. © 2014 Optical Society of America OCIS codes: (220.0220) Optical design and fabrication; (220.2945) Illumination design; (220.2740) Geometric optical design; (220.4610) Optical fabrication. http://dx.doi.org/10.1364/AO.53.005750
1. Introduction
High brightness and performance LEDs have been identified as the ideal light source for city lighting, especially in road lighting applications. Owing to their superiority in energy savings, long lifetime, environmental friendliness, and good color rendering, LEDs are replacing the traditionally used high pressure sodium (HPS) lamps as the most suitable light source in the latest generation of road lamps. In practice, energy-savings is not the only point one should take into account, considering that the essential purpose for road lighting is providing a comfortable lighting environment for drivers [1,2], which requires uniform illumination on the road surface and a low glare index. To maintain the advantages of LEDs while fulfilling the requirements 1559-128X/14/255750-05$15.00/0 © 2014 Optical Society of America 5750
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
of road lighting standards, special optical design techniques must be used. In this paper, we choose a chip-on-board (COB) [3] LED as the light source for road lamps. With multichip packaging, COB LEDs have lower packaging costs and can provide high power illumination as well as lower effects of pin light and glare. Due to integration, COB LEDs should be treated only as an extended source when designing its second stage optical system. In this paper, we design and propose a dual-module COB-LED-based high brightness street lamp that can offer uniform and effective rectangular illumination. Glare control has been considered in designing the maximum beam angle. In Section 2, details of the design of the street lamp will be presented. We have done some simulations based on Monte Carlo ray tracing and tested its prototype in verifying the simulation. In Section 3, we will evaluate the performance of the street lamp based on Chinese and European standards.
2. Optical Reflector Design
To realize the street lamp system, there are several different optical solutions, which may be reflectors, lenses, or reflective-refractive combinations. Objectively speaking, lenses have a stronger ability to control light rays—that is why lens design is very popular in LED secondary optics systems [4–6]. However, due to the total internal reflection (TIR) effects, Fresnel loss, and light absorbance loss, lenses could cause lower luminaire efficiency. For example, if Fresnel loss on one surface was 4.00%, the transmittance after two surfaces would decrease to 92.16%. With loss by TIR effects and absorbance added, the total efficiency would surely be less than 92.18%. To fulfill the efficiency potential of LED streetlamps, we propose a multifaceted free-form reflector to reflect and redistribute luminous flux in order to form the desired illumination distribution. The luminous flux on the targeted area consists only of direct incident flux and indirect incident flux. Thus, the loss will be caused only by the reflectance of the reflector. We use high-quality reflectors with reflectance of more than 98%. The total efficiency will probably be more than 95%, even after taking into account other kinds of losses. The 3D profile of the optical reflector and the rays’ directions are shown in Fig. 1(a). The reflector is composed of six facets; since there are two COB LED modules, the facets are arranged in bilateral symmetry. As we mentioned before, a COB LED should not be treated as a point source when designing the shape of the reflector. General free-form surface design techniques would meet failure for simplification of the light source. To achieve fine control over the distribution of luminous flux, we divide the imaginary flux space into several functional zones. First, the entire luminous flux space can be roughly separated into two zones—the direct incident area and the indirect incident area. Luminous flux in the former zone will be confined into a typical solid angle where all the light rays will be directed into the rectangular illuminated area. Light rays in the indirect incident zone will be reflected and heading toward the same area, with the luminous flux spread to form uniform illumination to compensate for the direct incident luminous flux. Second, the whole indirect incident zone is divided into several functional areas, with each faceted reflector responsible for one functional area. After that, we establish a mapping relationship between
Fig. 1. Comparison of 3D profiles and prototype of the street lamp. (a) 3D profile along with the rays’ directions, (b) prototype with power off, and (c) prototype of the optical reflector with power on.
the faceted reflectors and their target areas. There are six faceted reflectors—the D1, D2, D3, D4, D5, and D6 facets. The decision on the number of faceted reflectors is made by weighing the balance between the complexity of the structure and the flexibility of control over the luminous flux. The number of faceted reflectors should be at least enough to direct the luminous flux to the target illuminated area and form good uniformity. As we are dealing with extended sources, a single large facula could not guarantee good uniformity. With a number of faceted reflectors, a large facula can be cut into pieces and recombined to form a new pattern on the target area. It is obvious that, as the number of faceted reflectors increases, the reflectors will enjoy more flexibility and higher precision in control of the luminous flux, and, thus, the final illumination uniformity will be improved. However, the number is limited in practice due to the cost. In this paper, we choose the number of the faceted reflectors as six after giving consideration to both aspects. The divided faceted reflectors and their mapping relationship are presented in Fig. 2. Because of its bilateral symmetry, D1, D2, and D5 play the same roles as D4, D3, and D2, respectively. Take the left half as an instance: D1 and D5 direct the luminous flux spread uniformly into the left and middle bottom areas. Since the street lamp is designed to illuminate the left and right sides as well as the front, D2 has an outstretched shape and forms an overlapping pattern in the middle top area. To better understand how luminous flux of the LEDs is allocated and distributed in the target area, we present the front view of the street lamp in Fig. 3, which clearly illustrates this relationship. Point O refers to the middle position of the LEDs. Rays emitting from the center of LEDs form direct illuminated area AB. Marginal ray forms a maximum half-beam angle with the y axis. Point C indicates the middle point of area AB, and H is the height between the LEDs and the target illuminated area. We take
Fig. 2. Mapping relationship between the (a) faceted reflector and (b) the target areas on the road.
Fig. 3. Luminous flux allocation relationship between LEDs and the target area. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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two steps to design faceted reflectors. First, treat the LEDs as a whole and see their center point O as a virtual point source. The size and basic position of the six faceted reflectors are calculated based on this point source according to the flux conservation principle and the flux mapping relationship between the point light source space and the target area. Then the LEDs can be seen as extended sources, and fine tuning of the positions and angles of the faceted reflectors based on the marginal rays principle is needed. The marginal rays principle can help allocate the luminous flux from each functional area of light source space to the target illumination area. With this adjustment, luminous flux from the central beam of the LEDs can be confined in the effective target illuminated area so as to ensure high luminaire efficiency. Assuming the LEDs to be Lambert emitters, emergent rays approaching the normal direction take up more energy than those far from the normal direction, thus forming higher illuminance near the center area and a lower value near the side area. However, the case of the indirect emergent rays that are reflected by the faceted reflectors is the opposite. In Fig. 3, taking the left LED as an example, part of the emergent rays are reflected by the left reflector and form an indirect illuminated area. This time, emergent rays approaching the normal direction are reflected to the side area, while the rays incident to the center area carry less energy. In this way, the indirect incident rays compensate the direct incident rays of the luminous flux’s gaps and omissions. With six faceted reflectors, good control can be taken over the luminous flux to form uniform illumination in the target area. In Fig. 3, we set the angle between incident ray OPi and the y axis as θi, and the solid angle swept by incident ray OPi from the y axis OC can be expressed as dΩ 2π sin θdθ:
(1)
The output light intensity of an LED module is proportional to the product of luminance and the projected area of LED in the output direction: I LdS cos θ:
(2)
Luminous flux in the differential form is defined as dF IdΩ:
F πLAssin2 θD ρ1 − sin2 θD :
(5)
From Eqs. (1)–(4), we can obtain Eq. (5), which gives the relationship between outgoing luminous flux and θi , the angle between emergent ray OPi and the y axis. With angle θi varied from θD to 2π, point Ri moves from point C to point A, and, thus, rays incident to d are all reflected to area CA. By setting a arc ED proper mapping relationship between the length of CRi and angle θi , a specific illuminance distribution ! will be acquired. As we already know vectors OPi and ! Pi Ri , the position of point Pi xpi ; ypi can be easily derived based on the vector law of reflection. Finally, with enough position data of points Pi xpi ; ypi , the shape of the reflector can be obtained via curve fitting methods. As the street lamp is bilaterally symmetric but not symmetrical in its front and back sides, the actual construction of the reflector’s free-form surface must be dealt with in a 3D coordinate system. After we establish the mapping relationship between each functional space of the light source and the target illuminated area, as previously discussed, the energy allocated for each functional space is then determined. The points’ positions Pi xpi ; ypi ; zpi on the free-form surface of a faceted reflector can be derived by two steps. First, the curve fitted by points Pi xpi ; ypi is set as the root curve of the free-form surface. In this way, the coordinate value can be expressed as Pi xpi ; ypi ; 0. Second, we derive the points’ positions Pi xpi ; ypi ; zpi in the orthogonal direction of the root curve by applying Snell’s law in 3D coordinate space. The flux conservation principle and the flux mapping relationship expressed in 3D coordinates is used, as well. The final free-form surface is fitted in the software by non-uniform rational B-spline (NURBS) interpolation. Simulation and experimental results of the street lamp will be given in the next section. 3. Simulation and Experiment
We built the entire 3D model of the street lamp and conducted a simulation based on Monte Carlo ray tracing. The mounting height of the reflector is 10 m and the test area is 12 m wide and 30 m long. Figure 4(a) indicates the illumination distribution and Fig. 5 gives its value chart, which shows good
(3)
Based on Eqs. (1) and (2), we perform an integral of Eq. (3) and obtain Z F
Z
θD
ds 2πLdS sin θ cos θdθ As 0 Zπ Z 2 ds 2πLdS sin θ cos θdθ: ρ As
θD
(4)
Equation (4) is simplified to 5752
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
Fig. 4. Test results of simulation and experiment. (a) Illumination distribution and (b) candela distribution result based on simulation. (c) Candela distribution result based on actual measurement of the prototype.
Fig. 5. Value chart of the simulated illuminance pattern of the street lamp.
4. Conclusion
Fig. 6. Roadway illumination in zigzag arrangements.
uniformity of 0.62. Figure 4(b) refers to the candela distribution of the street lamp. We also do the actual measurement of the prototype. Figure 4(c) provides the tested candela distribution of the prototype. Figures 4(b) and 4(c) show similar candela distributions, but not the same. This may be caused by malposition of the light source in actual assembly or large matching tolerance of the reflector. To eliminate the difference, the assembly error of the LEDs should be restricted to within 0.2 mm. For the reflector, taking the central wavelength 550 nm as example, the result will be good if the matching tolerance can be confined into half of the wavelength, Table 1.
Zigzag
Double-side
a
which is about 275 nm in this case. In Figs. 4(b) and 4(c), the symmetric 0 deg curve shows that the maximum beam angle of the street lamp will be constrained at 70 deg, so it can meet the glare requirements of Chinese standard CJJ45-2006 [7] and European road lighting standards [8,9], which limit the candela value to 30 cd/klm at 80 deg and 10 cd/klm at 90 deg. In order to evaluate the road illuminance performance of the LED, we also carried out a roadway illumination simulation. For the simulation shown in Fig. 6, the mounting height of the street lamp is 10 m and the road width is 12 m. The distance between adjacent lamps on one side is 30 m. For a 100 W LED street lamp, which includes dual-module COB LED arrays, the power of each single-module COB LED array is 50 W. Comparison of the results of the simulation and the experiment are shown in Table 1. The average lux value in both the zigzag and normal double-side arrangements is 39 lux. The illumination uniformity (Emin ∕Eave ) is 0.62 in the zigzag configuration and 0.64 in the double-side arrangement, both of which are relatively high. In standard CJJ45-2006, the average luminance (cd∕m2 ) value is prescribed to be larger than 2.00 and the luminance uniformity (Lmin ∕Lave ) should be larger than 0.40. The simulation results show that the corresponding data are 2.65 and 0.55 in zigzag arrangements, while it is 2.65 and 0.58 in double-side arrangements; thus, both can meet the requirements.
We designed and proposed a faceted-reflector street lamp based on dual-module COB LEDs. Instead of dealing with the extended light source as a whole, which is difficult in optical design, we divided the luminous flux space into several functional areas and allocated the luminous flux of each functional area to the target area, thus achieving fine control over the emitted flux. The received luminous flux in the target area is composed of direct incident flux and indirect incident flux. We adjust the amount and target position of indirect luminous flux to form the final distribution of illumination. The allocation of luminous flux is achieved via reflection of different functional faceted reflectors, of which the size and basic position are calculated based on the flux
Comparison of Simulation and Experimental Results of Roadway Illuminationa
Lamp Arrangement
Minimum Expected Value
Simulation Results
Experimental Results
Uniformity of Illuminance Uniformity of luminance Average illuminance (lux) Average luminance (cd∕m2 ) Uniformity of Illuminance Uniformity of luminance Average illuminance (lux) Average luminance (cd∕m2 )
0.4 0.4 20/30 1.5/2.0 0.4 0.4 20/30 1.5/2.0
0.62 0.55 39.00 2.65 0.64 0.58 39.00 2.65
0.60 0.58 38.23 2.58 0.62 0.60 38.82 2.56
All under parameters of height = 10 m, road width = 12 m, and lamp spacing = 30 m. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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conservation principle and the flux mapping relationship. However, to get a good result, fine tuning of the faceted reflectors is conducted based on the marginal rays principle. After this, the entire luminous flux is confined in the effective target area with overlapped light spots, which compensate the flux gaps and omissions of each other. The street lamp, which is compact in size, effectively reduces the power consumption and provides uniform and wide illumination. The actual measurement results agree very well with the simulation results and both of them showed that the street lamp can meet the requirements of standard CJJ45-2006 and can even achieve better optical performance. Aiming Ge thanks the China Scholarship Council (CSC) for financial support through grant no. 2010610538 of his research study at Utah State University and the University of California, Merced. References 1. A. Haans and Y. A. W. de Kort, “Light distribution in dynamic street lighting: two experimental studies on its effects on perceived safety, prospect, concealment, and escape,” J. Environ. Psychol. 32, 342–352 (2012).
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2. R. Müllner and A. Riener, “An energy efficient pedestrian aware smart street lighting system,” Int. J. Pervas. Comput. Commun. 7, 147–161 (2011). 3. H. Yu, J. Shang, C. Xu, X. Luo, J. Liu, L. Zhang, and C. Lai, “Chip-on-board (COB) wafer level packaging of LEDs using silicon substrates and chemical foaming process (CFP)-made glass-bubble caps,” in 12th International Conference on Electronic Packaging Technology and High Density Packaging (ICEPT-HDP) (IEEE, 2011), pp. 1–4. 4. Z. Zheng, X. Hao, and X. Liu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. 48, 6627–6634 (2009). 5. K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A 11, 105501 (2009). 6. Y. C. Lo, K. T. Huang, X. H. Lee, and C. C. Sun, “Optical design of a butterfly lens for a street light based on a double-cluster LED,” Microelectron. Reliab. 52, 889–893 (2012). 7. CJJ45-2006, “Standard for lighting design of urban road” (2006), http://wenku.baidu.com/view/31a3112fcfc789eb172dc8ac .html. 8. “Code of practice for the design of road lighting: lighting of roads and public amenities,” British Standard BS 54891:2003, http://persona.uk.com/orga46newark/ha_docs/disposit_ docs/dd101‑dd200/dd164.pdf. 9. “Road lighting-performance requirements,” British Standard BS EN 13201-2:2003, http://www.doc88.com/p‑532791930330 .html.
Department of Light Sources and Illuminating Engineering, School of Information Science and Engineering, Institute for Electric Light Sources, Fudan University, Shanghai 200433, China 2
Dongguan CLED Optoelectronic Technology Co., Ltd, Dongguan 523270, China *Corresponding author: [email protected] Received 2 June 2014; revised 27 July 2014; accepted 28 July 2014; posted 31 July 2014 (Doc. ID 213230); published 28 August 2014
We design and propose a compact street lamp based on dual-module chip-on-board LED. The street lamp is composed of six faceted reflectors. It can direct the luminous flux and form uniform illumination on the target area, and it effectively reduces power consumption. We have conducted both simulations and prototype measurements. The test results show good optical performance in that the uniformity of luminance reaches 0.58 for LED lamp zigzag arrangements and 0.60 for LED lamp double-side arrangements. The average luminance can fulfill the requirements in Chinese road lighting Standard CJJ45-2006. © 2014 Optical Society of America OCIS codes: (220.0220) Optical design and fabrication; (220.2945) Illumination design; (220.2740) Geometric optical design; (220.4610) Optical fabrication. http://dx.doi.org/10.1364/AO.53.005750
1. Introduction
High brightness and performance LEDs have been identified as the ideal light source for city lighting, especially in road lighting applications. Owing to their superiority in energy savings, long lifetime, environmental friendliness, and good color rendering, LEDs are replacing the traditionally used high pressure sodium (HPS) lamps as the most suitable light source in the latest generation of road lamps. In practice, energy-savings is not the only point one should take into account, considering that the essential purpose for road lighting is providing a comfortable lighting environment for drivers [1,2], which requires uniform illumination on the road surface and a low glare index. To maintain the advantages of LEDs while fulfilling the requirements 1559-128X/14/255750-05$15.00/0 © 2014 Optical Society of America 5750
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
of road lighting standards, special optical design techniques must be used. In this paper, we choose a chip-on-board (COB) [3] LED as the light source for road lamps. With multichip packaging, COB LEDs have lower packaging costs and can provide high power illumination as well as lower effects of pin light and glare. Due to integration, COB LEDs should be treated only as an extended source when designing its second stage optical system. In this paper, we design and propose a dual-module COB-LED-based high brightness street lamp that can offer uniform and effective rectangular illumination. Glare control has been considered in designing the maximum beam angle. In Section 2, details of the design of the street lamp will be presented. We have done some simulations based on Monte Carlo ray tracing and tested its prototype in verifying the simulation. In Section 3, we will evaluate the performance of the street lamp based on Chinese and European standards.
2. Optical Reflector Design
To realize the street lamp system, there are several different optical solutions, which may be reflectors, lenses, or reflective-refractive combinations. Objectively speaking, lenses have a stronger ability to control light rays—that is why lens design is very popular in LED secondary optics systems [4–6]. However, due to the total internal reflection (TIR) effects, Fresnel loss, and light absorbance loss, lenses could cause lower luminaire efficiency. For example, if Fresnel loss on one surface was 4.00%, the transmittance after two surfaces would decrease to 92.16%. With loss by TIR effects and absorbance added, the total efficiency would surely be less than 92.18%. To fulfill the efficiency potential of LED streetlamps, we propose a multifaceted free-form reflector to reflect and redistribute luminous flux in order to form the desired illumination distribution. The luminous flux on the targeted area consists only of direct incident flux and indirect incident flux. Thus, the loss will be caused only by the reflectance of the reflector. We use high-quality reflectors with reflectance of more than 98%. The total efficiency will probably be more than 95%, even after taking into account other kinds of losses. The 3D profile of the optical reflector and the rays’ directions are shown in Fig. 1(a). The reflector is composed of six facets; since there are two COB LED modules, the facets are arranged in bilateral symmetry. As we mentioned before, a COB LED should not be treated as a point source when designing the shape of the reflector. General free-form surface design techniques would meet failure for simplification of the light source. To achieve fine control over the distribution of luminous flux, we divide the imaginary flux space into several functional zones. First, the entire luminous flux space can be roughly separated into two zones—the direct incident area and the indirect incident area. Luminous flux in the former zone will be confined into a typical solid angle where all the light rays will be directed into the rectangular illuminated area. Light rays in the indirect incident zone will be reflected and heading toward the same area, with the luminous flux spread to form uniform illumination to compensate for the direct incident luminous flux. Second, the whole indirect incident zone is divided into several functional areas, with each faceted reflector responsible for one functional area. After that, we establish a mapping relationship between
Fig. 1. Comparison of 3D profiles and prototype of the street lamp. (a) 3D profile along with the rays’ directions, (b) prototype with power off, and (c) prototype of the optical reflector with power on.
the faceted reflectors and their target areas. There are six faceted reflectors—the D1, D2, D3, D4, D5, and D6 facets. The decision on the number of faceted reflectors is made by weighing the balance between the complexity of the structure and the flexibility of control over the luminous flux. The number of faceted reflectors should be at least enough to direct the luminous flux to the target illuminated area and form good uniformity. As we are dealing with extended sources, a single large facula could not guarantee good uniformity. With a number of faceted reflectors, a large facula can be cut into pieces and recombined to form a new pattern on the target area. It is obvious that, as the number of faceted reflectors increases, the reflectors will enjoy more flexibility and higher precision in control of the luminous flux, and, thus, the final illumination uniformity will be improved. However, the number is limited in practice due to the cost. In this paper, we choose the number of the faceted reflectors as six after giving consideration to both aspects. The divided faceted reflectors and their mapping relationship are presented in Fig. 2. Because of its bilateral symmetry, D1, D2, and D5 play the same roles as D4, D3, and D2, respectively. Take the left half as an instance: D1 and D5 direct the luminous flux spread uniformly into the left and middle bottom areas. Since the street lamp is designed to illuminate the left and right sides as well as the front, D2 has an outstretched shape and forms an overlapping pattern in the middle top area. To better understand how luminous flux of the LEDs is allocated and distributed in the target area, we present the front view of the street lamp in Fig. 3, which clearly illustrates this relationship. Point O refers to the middle position of the LEDs. Rays emitting from the center of LEDs form direct illuminated area AB. Marginal ray forms a maximum half-beam angle with the y axis. Point C indicates the middle point of area AB, and H is the height between the LEDs and the target illuminated area. We take
Fig. 2. Mapping relationship between the (a) faceted reflector and (b) the target areas on the road.
Fig. 3. Luminous flux allocation relationship between LEDs and the target area. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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two steps to design faceted reflectors. First, treat the LEDs as a whole and see their center point O as a virtual point source. The size and basic position of the six faceted reflectors are calculated based on this point source according to the flux conservation principle and the flux mapping relationship between the point light source space and the target area. Then the LEDs can be seen as extended sources, and fine tuning of the positions and angles of the faceted reflectors based on the marginal rays principle is needed. The marginal rays principle can help allocate the luminous flux from each functional area of light source space to the target illumination area. With this adjustment, luminous flux from the central beam of the LEDs can be confined in the effective target illuminated area so as to ensure high luminaire efficiency. Assuming the LEDs to be Lambert emitters, emergent rays approaching the normal direction take up more energy than those far from the normal direction, thus forming higher illuminance near the center area and a lower value near the side area. However, the case of the indirect emergent rays that are reflected by the faceted reflectors is the opposite. In Fig. 3, taking the left LED as an example, part of the emergent rays are reflected by the left reflector and form an indirect illuminated area. This time, emergent rays approaching the normal direction are reflected to the side area, while the rays incident to the center area carry less energy. In this way, the indirect incident rays compensate the direct incident rays of the luminous flux’s gaps and omissions. With six faceted reflectors, good control can be taken over the luminous flux to form uniform illumination in the target area. In Fig. 3, we set the angle between incident ray OPi and the y axis as θi, and the solid angle swept by incident ray OPi from the y axis OC can be expressed as dΩ 2π sin θdθ:
(1)
The output light intensity of an LED module is proportional to the product of luminance and the projected area of LED in the output direction: I LdS cos θ:
(2)
Luminous flux in the differential form is defined as dF IdΩ:
F πLAssin2 θD ρ1 − sin2 θD :
(5)
From Eqs. (1)–(4), we can obtain Eq. (5), which gives the relationship between outgoing luminous flux and θi , the angle between emergent ray OPi and the y axis. With angle θi varied from θD to 2π, point Ri moves from point C to point A, and, thus, rays incident to d are all reflected to area CA. By setting a arc ED proper mapping relationship between the length of CRi and angle θi , a specific illuminance distribution ! will be acquired. As we already know vectors OPi and ! Pi Ri , the position of point Pi xpi ; ypi can be easily derived based on the vector law of reflection. Finally, with enough position data of points Pi xpi ; ypi , the shape of the reflector can be obtained via curve fitting methods. As the street lamp is bilaterally symmetric but not symmetrical in its front and back sides, the actual construction of the reflector’s free-form surface must be dealt with in a 3D coordinate system. After we establish the mapping relationship between each functional space of the light source and the target illuminated area, as previously discussed, the energy allocated for each functional space is then determined. The points’ positions Pi xpi ; ypi ; zpi on the free-form surface of a faceted reflector can be derived by two steps. First, the curve fitted by points Pi xpi ; ypi is set as the root curve of the free-form surface. In this way, the coordinate value can be expressed as Pi xpi ; ypi ; 0. Second, we derive the points’ positions Pi xpi ; ypi ; zpi in the orthogonal direction of the root curve by applying Snell’s law in 3D coordinate space. The flux conservation principle and the flux mapping relationship expressed in 3D coordinates is used, as well. The final free-form surface is fitted in the software by non-uniform rational B-spline (NURBS) interpolation. Simulation and experimental results of the street lamp will be given in the next section. 3. Simulation and Experiment
We built the entire 3D model of the street lamp and conducted a simulation based on Monte Carlo ray tracing. The mounting height of the reflector is 10 m and the test area is 12 m wide and 30 m long. Figure 4(a) indicates the illumination distribution and Fig. 5 gives its value chart, which shows good
(3)
Based on Eqs. (1) and (2), we perform an integral of Eq. (3) and obtain Z F
Z
θD
ds 2πLdS sin θ cos θdθ As 0 Zπ Z 2 ds 2πLdS sin θ cos θdθ: ρ As
θD
(4)
Equation (4) is simplified to 5752
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
Fig. 4. Test results of simulation and experiment. (a) Illumination distribution and (b) candela distribution result based on simulation. (c) Candela distribution result based on actual measurement of the prototype.
Fig. 5. Value chart of the simulated illuminance pattern of the street lamp.
4. Conclusion
Fig. 6. Roadway illumination in zigzag arrangements.
uniformity of 0.62. Figure 4(b) refers to the candela distribution of the street lamp. We also do the actual measurement of the prototype. Figure 4(c) provides the tested candela distribution of the prototype. Figures 4(b) and 4(c) show similar candela distributions, but not the same. This may be caused by malposition of the light source in actual assembly or large matching tolerance of the reflector. To eliminate the difference, the assembly error of the LEDs should be restricted to within 0.2 mm. For the reflector, taking the central wavelength 550 nm as example, the result will be good if the matching tolerance can be confined into half of the wavelength, Table 1.
Zigzag
Double-side
a
which is about 275 nm in this case. In Figs. 4(b) and 4(c), the symmetric 0 deg curve shows that the maximum beam angle of the street lamp will be constrained at 70 deg, so it can meet the glare requirements of Chinese standard CJJ45-2006 [7] and European road lighting standards [8,9], which limit the candela value to 30 cd/klm at 80 deg and 10 cd/klm at 90 deg. In order to evaluate the road illuminance performance of the LED, we also carried out a roadway illumination simulation. For the simulation shown in Fig. 6, the mounting height of the street lamp is 10 m and the road width is 12 m. The distance between adjacent lamps on one side is 30 m. For a 100 W LED street lamp, which includes dual-module COB LED arrays, the power of each single-module COB LED array is 50 W. Comparison of the results of the simulation and the experiment are shown in Table 1. The average lux value in both the zigzag and normal double-side arrangements is 39 lux. The illumination uniformity (Emin ∕Eave ) is 0.62 in the zigzag configuration and 0.64 in the double-side arrangement, both of which are relatively high. In standard CJJ45-2006, the average luminance (cd∕m2 ) value is prescribed to be larger than 2.00 and the luminance uniformity (Lmin ∕Lave ) should be larger than 0.40. The simulation results show that the corresponding data are 2.65 and 0.55 in zigzag arrangements, while it is 2.65 and 0.58 in double-side arrangements; thus, both can meet the requirements.
We designed and proposed a faceted-reflector street lamp based on dual-module COB LEDs. Instead of dealing with the extended light source as a whole, which is difficult in optical design, we divided the luminous flux space into several functional areas and allocated the luminous flux of each functional area to the target area, thus achieving fine control over the emitted flux. The received luminous flux in the target area is composed of direct incident flux and indirect incident flux. We adjust the amount and target position of indirect luminous flux to form the final distribution of illumination. The allocation of luminous flux is achieved via reflection of different functional faceted reflectors, of which the size and basic position are calculated based on the flux
Comparison of Simulation and Experimental Results of Roadway Illuminationa
Lamp Arrangement
Minimum Expected Value
Simulation Results
Experimental Results
Uniformity of Illuminance Uniformity of luminance Average illuminance (lux) Average luminance (cd∕m2 ) Uniformity of Illuminance Uniformity of luminance Average illuminance (lux) Average luminance (cd∕m2 )
0.4 0.4 20/30 1.5/2.0 0.4 0.4 20/30 1.5/2.0
0.62 0.55 39.00 2.65 0.64 0.58 39.00 2.65
0.60 0.58 38.23 2.58 0.62 0.60 38.82 2.56
All under parameters of height = 10 m, road width = 12 m, and lamp spacing = 30 m. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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conservation principle and the flux mapping relationship. However, to get a good result, fine tuning of the faceted reflectors is conducted based on the marginal rays principle. After this, the entire luminous flux is confined in the effective target area with overlapped light spots, which compensate the flux gaps and omissions of each other. The street lamp, which is compact in size, effectively reduces the power consumption and provides uniform and wide illumination. The actual measurement results agree very well with the simulation results and both of them showed that the street lamp can meet the requirements of standard CJJ45-2006 and can even achieve better optical performance. Aiming Ge thanks the China Scholarship Council (CSC) for financial support through grant no. 2010610538 of his research study at Utah State University and the University of California, Merced. References 1. A. Haans and Y. A. W. de Kort, “Light distribution in dynamic street lighting: two experimental studies on its effects on perceived safety, prospect, concealment, and escape,” J. Environ. Psychol. 32, 342–352 (2012).
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2. R. Müllner and A. Riener, “An energy efficient pedestrian aware smart street lighting system,” Int. J. Pervas. Comput. Commun. 7, 147–161 (2011). 3. H. Yu, J. Shang, C. Xu, X. Luo, J. Liu, L. Zhang, and C. Lai, “Chip-on-board (COB) wafer level packaging of LEDs using silicon substrates and chemical foaming process (CFP)-made glass-bubble caps,” in 12th International Conference on Electronic Packaging Technology and High Density Packaging (ICEPT-HDP) (IEEE, 2011), pp. 1–4. 4. Z. Zheng, X. Hao, and X. Liu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. 48, 6627–6634 (2009). 5. K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A 11, 105501 (2009). 6. Y. C. Lo, K. T. Huang, X. H. Lee, and C. C. Sun, “Optical design of a butterfly lens for a street light based on a double-cluster LED,” Microelectron. Reliab. 52, 889–893 (2012). 7. CJJ45-2006, “Standard for lighting design of urban road” (2006), http://wenku.baidu.com/view/31a3112fcfc789eb172dc8ac .html. 8. “Code of practice for the design of road lighting: lighting of roads and public amenities,” British Standard BS 54891:2003, http://persona.uk.com/orga46newark/ha_docs/disposit_ docs/dd101‑dd200/dd164.pdf. 9. “Road lighting-performance requirements,” British Standard BS EN 13201-2:2003, http://www.doc88.com/p‑532791930330 .html.
